Abstract: [Special Room 3088 East Hall.]
The use of ideas from topology to to inspire algebraic and algebro-geometric constructions has played an important role throughout the history of algebraic geometry. Some well-known examples of this include enumerative geometry and the theory of algebraic cycles and algebraic K-theory. In the 90's Morel and Voevodsky constructed a number of categories which allow one to systematically import ideas from homotopy theory to algebraic geometry, creating the field now known as motivic homotopy theory. We will give some idea of this theory, describe some interesting constructions arising out of the theory and talk about applications and open questions. (Spring Lectures in Algebraic Geometry)